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It would be borderline disrespectful to refer to these current Celtics as the “Big Three’’ now. The emergence of Rajon Rondo and the addition yesterday of one rather sizable player changed that for good.

The Celtics will enter the upcoming season with nearly as much sizzle as their counterparts in Miami, as NBA icon, all-time great center, and Hall of Fame personality Shaquille O’Neal signed a two-year, $2.8 million contract with Boston, his sixth team in an illustrious but rocky career.

O’Neal has four NBA championship rings — three with the Lakers and one with the Heat — but he has left most of his previous teams with hard feelings, as he has been prone to clash with teammates and eventually wear out his welcome.

So with the Celtics having so many strong personalities and being an organization that makes team chemistry a priority, the signing of the 38-year-old center could be a risky move.

Yet if O’Neal blends into the system, they could have a defen sive and physical answer for most of their top rivals. When healthy and focused, O’Neal remains a skilled center who can draw double-teams — something Kendrick Perkins has yet to accomplish — and open up the floor for Paul Pierce and Ray Allen.

“It is not every day that you can add a player of Shaquille’s caliber to your team,’’ said Celtics president Danny Ainge in a statement. “His past experience speaks for itself and we believe that he is a great fit for our roster, so we’re very excited that he is joining the Celtics family.

“Some have questioned his effectiveness, but last year Shaquille was still one of the league’s better defensive rebounders. This will address a weakness of ours during last year’s regular season. In addition to rebounding, Shaq brings post scoring, toughness, and a winning spirit.

“I remember in 1985, we signed Bill Walton, and his addition put us over the top. We feel that with the addition of Shaq, we’ll have one of the best front lines in the league, and, when Kendrick Perkins returns, the deepest.

“Shaq has made it clear that he would do whatever it takes to help the team raise Banner 18, and we look forward to working towards that goal together.’’

Many questions won’t be answered until training camp. Will he start? Can he play with Kevin Garnett? How many shots will he demand? And what exactly will the Boston faithful call him?

Celtics fans have two months to come up with a nickname before O’Neal reports to training camp, though the organization appeared thrilled simply to acquire “The Big To Be Determined.’’

“I am very excited,’’ said coach Doc Rivers, who met with O’Neal in Orlando, Fla. “Adding a player like Shaq is a major plus and it fills a void for our team. He’s a real nice piece of the puzzle and he will complement us in where we want to go this coming season.’’

O’Neal wanted a multiyear contract in the neighborhood of $10 million, but teams passed on those demands, especially given the Big Aristotle’s history of making waves when unsatisfied with his role. So a month into free agency, he was reduced to lobbying for a role in Boston or perhaps heading to Atlanta for slightly more money.

All Ainge had to offer was the veteran minimum of $1.35 million, and O’Neal compromised by accepting that on a two-year deal. He often has said in recent years that he’d like to play until he’s 40, and this deal will conclude a few months beyond his 40th birthday.

“We have reloaded to defend our Eastern championship and try to contend for a title,’’ said Celtics principal owner Wyc Grousbeck. “With Shaq and Jermaine [O’Neal] added to Rondo and our Big Three, we ought to be a tough team.’’

O’Neal averaged 12 points and 6.7 rebounds in just 23.4 minutes per game last season with the Cavaliers. And he averaged 13.5 points in the Eastern Conference semifinals against Boston, a series overshadowed by the curious performance of LeBron James.

The Celtics potentially could have worked out a sign-and-trade deal with the Cavaliers to give O’Neal more money, but they preferred to hold on to the trade chip of Rasheed Wallace’s contract and give O’Neal an additional year.

“I am honored to be joining the Celtics,’’ O’Neal said in a statement. “I have played against Paul, Ray, Kevin, Rajon, and Jermaine for many years and it will be great to be able to call them my teammates. I cannot wait to get to Boston to get started in pursuit of another championship.’’

Those close to O’Neal believe he will come to Boston on his best behavior and that he respects the history of the organization. The 15-time All-Star immediately becomes one of the bigger personalities in team history.

With his bright smile, plethora of tattoos, and numerous nicknames, O’Neal should add spice. He is also credited with giving Pierce the nickname “The Truth’’ following a 2001 game between the Celtics and Lakers.

The Celtics are now stacked in the frontcourt with the two O’Neals, Garnett, Glen Davis, Luke Harangody, Semih Erden, and Perkins (who will miss part of the season because of knee surgery). And they appear ready for at least one more title charge.

“All we have to do is improve by six minutes,’’ said Celtics co-owner Robert Epstein, referring to the blown lead in Game 7 of the NBA Finals. “I think it’s exciting for everybody to contemplate the possibility of [O’Neal]. He’s already a legend. He’s a playing legend.’’